optimization value not able to acheive

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Kundan Prasad 2021-12-8

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评论： Kundan Prasad 2021-12-17

I am not able to get the optimize value of n. Every time it shows Failure in initial objective function evaluation. FSOLVE cannot continue

Below matlab code is given. Thank you

Function

clear all

clc

function F = roo2d(n)

F=[(sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2-0.31;

(sin(pi*((n(1)/1100)-1))/(pi*((n(1)/700)-1)))^2-0.42;

(sin(pi*((n(1)/1500)-1))/(pi*((n(1)/700)-1)))^2-0.50;

(sin(pi*((n(1)/2000)-1))/(pi*((n(1)/700)-1)))^2-0.59;

(sin(pi*((n(1)/2500)-1))/(pi*((n(1)/700)-1)))^2-0.64;

(sin(pi*((n(1)/3000)-1))/(pi*((n(1)/700)-1)))^2-0.655;

(sin(pi*((n(1)/3500)-1))/(pi*((n(1)/700)-1)))^2-0.64;

(sin(pi*((n(1)/4000)-1))/(pi*((n(1)/700)-1)))^2-0.59;

(sin(pi*((n(1)/4500)-1))/(pi*((n(1)/700)-1)))^2-0.50;

(sin(pi*((n(1)/5000)-1))/(pi*((n(1)/700)-1)))^2-0.39];

end

calling a function

fun= @roo2d

n0=[2000];

options = optimoptions('fsolve','Algorithm','levenberg-marquardt');

x= fsolve(fun,n0,options);

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Answer 1

Walter Roberson 2021-12-9

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All of your equations are effectively

calculations --

just with an offset for where the effective zero point is.

sinc() has a central spike that hits 1, but outside of that central spike, it never gets above

for the original function -- the square of that for

. So when you subtract values like 0.59, unless you are subtracting values down near 0.025 or less, then each of the functions individually has exactly two solutions, one before its central peak and one after its central peak.

With you using different divisors, you are guaranting that those central peaks do not line up -- and thus that only one function at a time has a solution. You can be certain that there is no possible solution for all of the functions simultaneously.

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Walter Roberson 2021-12-13

在 MATLAB Online 中打开

The problem that you had was that your initial point was exactly where one of the components is numerically undefined. You divide by (pi * (n(1)/2000-1)) but that is pi * 0 when n(1) = 2000 exactly, and that gives you the NaN.

format long g
[sol, fval] = fsolve(@roo2d, 2001)
Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.
No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function
values is not near zero, as measured by the value of the function tolerance. 
sol = 
          2277.41645109099
fval = 10×1
        -0.299807234490496
        -0.415746780114875
        -0.124039174417467
          0.34828407762878
         0.334191903268672
         0.168131040891419
        0.0177767363362461
       -0.0691924368700483
       -0.0848070434951021
       -0.0549144920748943
function F = roo2d(n)
F=[(sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2-0.31;
    (sin(pi*((n(1)/1100)-1))/(pi*((n(1)/1100)-1)))^2-0.42;
    (sin(pi*((n(1)/1500)-1))/(pi*((n(1)/1500)-1)))^2-0.50;
    (sin(pi*((n(1)/2000)-1))/(pi*((n(1)/2000)-1)))^2-0.59;
    (sin(pi*((n(1)/2500)-1))/(pi*((n(1)/2500)-1)))^2-0.64;
    (sin(pi*((n(1)/3000)-1))/(pi*((n(1)/3000)-1)))^2-0.655;
    (sin(pi*((n(1)/3500)-1))/(pi*((n(1)/3500)-1)))^2-0.64;
    (sin(pi*((n(1)/4000)-1))/(pi*((n(1)/4000)-1)))^2-0.59;
    (sin(pi*((n(1)/4500)-1))/(pi*((n(1)/4500)-1)))^2-0.50;
    (sin(pi*((n(1)/5000)-1))/(pi*((n(1)/5000)-1)))^2-0.39];
end

Kundan Prasad 2021-12-15

在 MATLAB Online 中打开

Sir i am facing problem for optimization of dual blaze wavelenght.

the code is given below

N=[linspace(700,5000,500) linspace(0,0.5,0.01)];
% N= linspace(700,5000,0.5)
y = cell2mat(arrayfun(@roo2d, N, 'uniform', 0));
plot(N, y.');
yline(0, 'k')
format long g
[sol, fval] = fsolve(@roo2d, 2001)
function F = roo2d(n)
F=[((sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2)*n(3)+...
((sin(pi*((n(2)/700)-1))/(pi*((n(2)/700)-1)))^2)*n(4)-0.31;
((sin(pi*((n(1)/1100)-1))/(pi*((n(1)/1100)-1)))^2)*n(3)+...
((sin(pi*((n(2)/1100)-1))/(pi*((n(2)/1100)-1)))^2)*n(4)-0.42;
((sin(pi*((n(1)/1500)-1))/(pi*((n(1)/1500)-1)))^2)*n(3)+....
((sin(pi*((n(2)/1500)-1))/(pi*((n(2)/1500)-1)))^2)*n(4)-0.50;
((sin(pi*((n(1)/2000)-1))/(pi*((n(1)/2000)-1)))^2)*n(3)+.....
((sin(pi*((n(2)/2000)-1))/(pi*((n(2)/2000)-1)))^2)*n(4)-0.59;
((sin(pi*((n(1)/2500)-1))/(pi*((n(1)/2500)-1)))^2)*n(3)+......
((sin(pi*((n(2)/2500)-1))/(pi*((n(2)/2500)-1)))^2)*n(4)-0.64;
((sin(pi*((n(1)/3000)-1))/(pi*((n(1)/3000)-1)))^2)*n(3)+.....
((sin(pi*((n(2)/3000)-1))/(pi*((n(2)/3000)-1)))^2)*n(4)-0.655;
((sin(pi*((n(1)/3500)-1))/(pi*((n(1)/3500)-1)))^2)*n(3)+....
((sin(pi*((n(2)/3500)-1))/(pi*((n(2)/3500)-1)))^2)*n(4)-0.64;
((sin(pi*((n(1)/4000)-1))/(pi*((n(1)/4000)-1)))^2)*n(3)+.....
((sin(pi*((n(2)/4000)-1))/(pi*((n(2)/4000)-1)))^2)*n(4)-0.59;
((sin(pi*((n(1)/4500)-1))/(pi*((n(1)/4500)-1)))^2)*n(3)+.....
((sin(pi*((n(2)/4500)-1))/(pi*((n(2)/4500)-1)))^2)*n(4)-0.50;
((sin(pi*((n(1)/5000)-1))/(pi*((n(1)/5000)-1)))^2)*n(3)+.....
((sin(pi*((n(2)/5000)-1))/(pi*((n(2)/5000)-1)))^2)*n(4)-0.39;
abs(n(3));
abs(n(4));
n(3)+n(4)-1];
       
end

Walter Roberson 2021-12-15

编辑：Walter Roberson 2021-12-15

在 MATLAB Online 中打开

N=[linspace(700,5000,500) linspace(0,0.5,0.01)];

% N= linspace(700,5000,0.5)

y = cell2mat(arrayfun(@(n)roo2d(n*ones(1,4)), N, 'uniform', 0));

plot(N, y.');

yline(0, 'k')

legend(cellstr(string(1:13)), 'location', 'best')

format long g

[sol, fval] = fsolve(@roo2d, 2001*ones(1,4))

Warning: Trust-region-dogleg algorithm of FSOLVE cannot handle non-square systems; using Levenberg-Marquardt algorithm instead.

No solution found. fsolve stopped because the problem appears regular as measured by the gradient, but the vector of function values is not near zero as measured by the value of the function tolerance.

sol = 1×4

1.0e+00 * 3160.55329192195 1540.72536365328 0.443793615705221 0.442783020449565

fval = 13×1

-0.295527268338015 -0.164947303712957 -0.0542950346625865 -0.0936715674976596 -0.023400832165584 -0.0261077254100426 -0.0715981375285406 -0.102994370069773 -0.0910707384428546 -0.0481765550137346

function F = roo2d(n)

F=[((sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2)*n(3)+...

((sin(pi*((n(2)/700)-1))/(pi*((n(2)/700)-1)))^2)*n(4)-0.31;

((sin(pi*((n(1)/1100)-1))/(pi*((n(1)/1100)-1)))^2)*n(3)+...

((sin(pi*((n(2)/1100)-1))/(pi*((n(2)/1100)-1)))^2)*n(4)-0.42;

((sin(pi*((n(1)/1500)-1))/(pi*((n(1)/1500)-1)))^2)*n(3)+....

((sin(pi*((n(2)/1500)-1))/(pi*((n(2)/1500)-1)))^2)*n(4)-0.50;

((sin(pi*((n(1)/2000)-1))/(pi*((n(1)/2000)-1)))^2)*n(3)+.....

((sin(pi*((n(2)/2000)-1))/(pi*((n(2)/2000)-1)))^2)*n(4)-0.59;

((sin(pi*((n(1)/2500)-1))/(pi*((n(1)/2500)-1)))^2)*n(3)+......

((sin(pi*((n(2)/2500)-1))/(pi*((n(2)/2500)-1)))^2)*n(4)-0.64;

((sin(pi*((n(1)/3000)-1))/(pi*((n(1)/3000)-1)))^2)*n(3)+.....

((sin(pi*((n(2)/3000)-1))/(pi*((n(2)/3000)-1)))^2)*n(4)-0.655;

((sin(pi*((n(1)/3500)-1))/(pi*((n(1)/3500)-1)))^2)*n(3)+....

((sin(pi*((n(2)/3500)-1))/(pi*((n(2)/3500)-1)))^2)*n(4)-0.64;

((sin(pi*((n(1)/4000)-1))/(pi*((n(1)/4000)-1)))^2)*n(3)+.....

((sin(pi*((n(2)/4000)-1))/(pi*((n(2)/4000)-1)))^2)*n(4)-0.59;

((sin(pi*((n(1)/4500)-1))/(pi*((n(1)/4500)-1)))^2)*n(3)+.....

((sin(pi*((n(2)/4500)-1))/(pi*((n(2)/4500)-1)))^2)*n(4)-0.50;

((sin(pi*((n(1)/5000)-1))/(pi*((n(1)/5000)-1)))^2)*n(3)+.....

((sin(pi*((n(2)/5000)-1))/(pi*((n(2)/5000)-1)))^2)*n(4)-0.39;

abs(n(3));

abs(n(4));

n(3)+n(4)-1];

end

Kundan Prasad 2021-12-17

Thank you sir,

Now I am able achieve the optimization for more than two number of blaze wavelength

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Answer 2

Alan Weiss 2021-12-8

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That is not what I get when I run your code:

No solution found.

fsolve stopped because the last step was ineffective. However, the vector of function

values is not near zero, as measured by the value of the function tolerance.

Sometiimes it is worthwhile plotting your function to see whether it might have some roots.

t = linspace(800,1e3);

z = zeros(10,length(t));

for i = 1:length(t)

z(:,i) = roo2d(t(i));

end

plot(t,z)

figure

t = linspace(1e3,3e3);

z = zeros(10,length(t));

for i = 1:length(t)

z(:,i) = roo2d(t(i));

end

plot(t,z)

function F = roo2d(n)

F=[(sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2-0.31;

(sin(pi*((n(1)/1100)-1))/(pi*((n(1)/700)-1)))^2-0.42;

(sin(pi*((n(1)/1500)-1))/(pi*((n(1)/700)-1)))^2-0.50;

(sin(pi*((n(1)/2000)-1))/(pi*((n(1)/700)-1)))^2-0.59;

(sin(pi*((n(1)/2500)-1))/(pi*((n(1)/700)-1)))^2-0.64;

(sin(pi*((n(1)/3000)-1))/(pi*((n(1)/700)-1)))^2-0.655;

(sin(pi*((n(1)/3500)-1))/(pi*((n(1)/700)-1)))^2-0.64;

(sin(pi*((n(1)/4000)-1))/(pi*((n(1)/700)-1)))^2-0.59;

(sin(pi*((n(1)/4500)-1))/(pi*((n(1)/700)-1)))^2-0.50;

(sin(pi*((n(1)/5000)-1))/(pi*((n(1)/700)-1)))^2-0.39];

end

There is clearly no time t where all of the curves simultaneously cross 0.

Alan Weiss

MATLAB mathematical toolbox documentation

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Kundan Prasad 2021-12-9

编辑：Walter Roberson 2021-12-9

在 MATLAB Online 中打开

I have made mistake in function value and have corrected the same. But still i am not able to get the optimized value of n as 2277

function F = roo2d(n)
F=[(sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2-0.31;
    (sin(pi*((n(1)/1100)-1))/(pi*((n(1)/1100)-1)))^2-0.42;
    (sin(pi*((n(1)/1500)-1))/(pi*((n(1)/1500)-1)))^2-0.50;
    (sin(pi*((n(1)/2000)-1))/(pi*((n(1)/2000)-1)))^2-0.59;
    (sin(pi*((n(1)/2500)-1))/(pi*((n(1)/2500)-1)))^2-0.64;
    (sin(pi*((n(1)/3000)-1))/(pi*((n(1)/3000)-1)))^2-0.655;
    (sin(pi*((n(1)/3500)-1))/(pi*((n(1)/3500)-1)))^2-0.64;
    (sin(pi*((n(1)/4000)-1))/(pi*((n(1)/4000)-1)))^2-0.59;
    (sin(pi*((n(1)/4500)-1))/(pi*((n(1)/4500)-1)))^2-0.50;
    (sin(pi*((n(1)/5000)-1))/(pi*((n(1)/5000)-1)))^2-0.39];
end

Walter Roberson 2021-12-9

在 MATLAB Online 中打开

N = linspace(2000,2500,500);

y = cell2mat(arrayfun(@roo2d, N, 'uniform', 0));

plot(N, y.');

yline(0, 'k')

function F = roo2d(n)

F=[(sin(pi*((n(1)/700)-1))/(pi*((n(1)/700)-1)))^2-0.31;

(sin(pi*((n(1)/1100)-1))/(pi*((n(1)/1100)-1)))^2-0.42;

(sin(pi*((n(1)/1500)-1))/(pi*((n(1)/1500)-1)))^2-0.50;

(sin(pi*((n(1)/2000)-1))/(pi*((n(1)/2000)-1)))^2-0.59;

(sin(pi*((n(1)/2500)-1))/(pi*((n(1)/2500)-1)))^2-0.64;

(sin(pi*((n(1)/3000)-1))/(pi*((n(1)/3000)-1)))^2-0.655;

(sin(pi*((n(1)/3500)-1))/(pi*((n(1)/3500)-1)))^2-0.64;

(sin(pi*((n(1)/4000)-1))/(pi*((n(1)/4000)-1)))^2-0.59;

(sin(pi*((n(1)/4500)-1))/(pi*((n(1)/4500)-1)))^2-0.50;

(sin(pi*((n(1)/5000)-1))/(pi*((n(1)/5000)-1)))^2-0.39];

end

Look at the graph. Near 2250-ish, it crosses 0 for one of the functions -- but when you fsolve() you are asking for all of the functions to be solved.

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optimization value not able to acheive

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optimization value not able to acheive

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